# Quantization of derived cotangent stacks and gauge theory on directed graphs

January 25, 2022

We study the quantization of the canonical unshifted Poisson structure on the
derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a
smooth affine scheme with an action of a (reductive) smooth affine group scheme
$G$. This is achieved through an \'etale resolution of $T^\ast[X/G]$ by stacky
CDGAs that allows for an explicit description of the canonical Poisson
structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it.
These techniques are applied to construct a dg-category-valued prefactorization
algebra that quantizes a gauge theory on directed graphs.

Keywords:

Derived algebraic geometry, derived cotangent stack, quotient stack, Deformation quantization, lattice gauge theory